College_GPA HS_GPA
College_GPA 1.0000000 0.5630064
HS_GPA 0.5630064 1.0000000Career Choice and Academic Performance
Chris Cioffi, Kristina Frazier, Aidan Hennessy, Mike McHenry
Overview
- Introduction and Question
- Background and Related Literature
- Data
- Exploratory Analysis
- Modeling
- Diagnostic Tools
- Remedial Measures
- Conclusion
What Do You Want to Be When You Grow Up?
During high school, young adults are often asked to make decisions regarding post-secondary education that can have a profound and lasting impact on their lives in the future.
We investigate what factors in high school may be related to future academic performance.
Research Question
Question: How is college GPA related to prospective career path in high school? How are other characteristics about a student’s background and high school environment related to their college GPA?
This study aims to investigate whether students who have a desired future career path in the 9th grade perform better than students who do not, and if choice of career path matters.
Data
- High School Longitudinal Study of 2009 (HSLS:09) from the National Center for Education Statistics.
- Interviewed 9th graders across the United States in 2009.
- Followed up with subjects in three subsequent interview rounds.
- Offers a variety of information on students, parents, and school.
Key Variables
Response Variable: College GPA
Primary Predictor of Interest: Desired occupation at age 30.
- A categorical variable with 22 occupation groups.
Additional predictors:
- Academic: High school GPA, credits earned for AP/IB courses, School engagement, Stem/non-stem desired occupation
- Geographic and Socioeconomic Factors: Family Income, High School urbanicity, High School type
A Look at Desired Occupation
Desired Occupation and Academic Performance
Color-coded by Planned student occupation at age 30
Model: Simple Linear Regression
Set reference group to those students who answered “Don’t Know”.
Model takes the form of \(College\_GPA = \beta_0 + \beta_1future\_job + \epsilon\).
Results: Simple Linear Regression
- Showing only results with a p-value < 0.10.
# A tibble: 7 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 2.72 0.0170 160. 0
2 Education, Training, and Library Occupat… 0.192 0.0454 4.24 2.28e-5
3 Arts, Design, Entertainment, Sports, and… -0.109 0.0303 -3.60 3.16e-4
4 Protective Service Occupations -0.317 0.0595 -5.33 1.00e-7
5 Food Preparation and Serving Related Occ… -0.329 0.0878 -3.75 1.79e-4
6 Installation, Maintenance, and Repair Oc… -0.271 0.104 -2.62 8.84e-3
7 Military Specific Occupations -0.358 0.0725 -4.94 8.08e-7- Adjusted \(R^2\) is less than 1%.
Additional Variables
Additional Variables
Additional Variables
Additional Variables
Multiple Linear Regression
Initial MLR Model: \[College\_GPA = \\ \beta_0 + \beta_1future\_job + \beta_2college\_gpa + \beta_3major\_considering + \\ \beta_4family\_income + \beta_5credits + \beta_6school\_type + \beta_7urbanicity + \\ \beta_8school\_belonging + \epsilon\]
- Adjusted \(R^2\): 0.3563
- F-statistic: 66.59 on 62 and 7286 DF, p-value: < 2.2e-16
Remove Urbanicity & School Belonging?
- Urbanicity & School Belonging: All Betas are insignificant at alpha = 0.10
Lack of Fit Test
Null Hypothesis: \(\beta_7urbanicity\) = \(\beta_8school\_belonging\) = 0
Alternative hypothesis: either of the betas for these variables is a non-zero value
Use alpha = 0.10
Remove Urbanicity & School Belonging?
Analysis of Variance Table
Model 1: X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 + X1FAMINCOME +
X3TCREDAPIB + X1CONTROL
Model 2: X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 + X1LOCALE +
X1FAMINCOME + X3TCREDAPIB + X1CONTROL + X1SCHOOLBEL
Res.Df RSS Df Sum of Sq F Pr(>F)
1 7290 3608.0
2 7286 3605.7 4 2.2764 1.15 0.331With a P-value of 0.331, there is insufficient evidence to reject the null hypothesis that the values for the betas of these two predictors are not zero.
The lack of significant relationship between Urbanicity & School Belonging was seen in earlier plots.
Variable Selection
New MLR Model: \[College\_GPA = \\ \beta_0 + \beta_1future\_job + \beta_2college\_gpa + \beta_3major\_considering + \\ \beta_4family\_income + \beta_5credits + \beta_6school\_type + \epsilon\]
- Stepwise selection did not remove additional variables
Diagnostics
Linearity
- F-statistic: 71.1 on 58 and 7290 DF, p-value: < 2.2e-16
Call:
lm(formula = X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 +
X1FAMINCOME + X3TCREDAPIB + X1CONTROL, data = MLR_all)
Residuals:
Min 1Q Median 3Q Max
-3.11365 -0.34477 0.09234 0.43827 2.75491
Coefficients:
Estimate
(Intercept) 0.4541565
X1STU30OCC2Management Occupations 0.0153304
X1STU30OCC2Business and Financial Operations Occupations 0.0782835
X1STU30OCC2Computer and Mathematical Occupations -0.0370277
X1STU30OCC2Architecture and Engineering Occupations -0.0585375
X1STU30OCC2Life, Physical, and Social Science Occupations -0.0304988
X1STU30OCC2Community and Social Services Occupations 0.1392815
X1STU30OCC2Legal Occupations -0.0737682
X1STU30OCC2Education, Training, and Library Occupations 0.0670447
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations -0.0050668
X1STU30OCC2Healthcare Practitioners and Technical Occupations -0.0302980
X1STU30OCC2Healthcare Support Occupations 0.0869059
X1STU30OCC2Protective Service Occupations -0.0524724
X1STU30OCC2Food Preparation and Serving Related Occupations -0.2356375
X1STU30OCC2Personal Care and Service Occupations 0.0982343
X1STU30OCC2Sales and Related Occupations 0.0434307
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.1171752
X1STU30OCC2Construction and Extraction Occupations 0.0705477
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.1269173
X1STU30OCC2Production Occupations 0.1494096
X1STU30OCC2Transportation and Material Moving Occupations 0.1271622
X1STU30OCC2Military Specific Occupations -0.1665261
X3TGPAACAD 0.6807046
X4ENTRYMAJ23Computer and information sciences -0.0041207
X4ENTRYMAJ23Engineering and engineering technology 0.0002693
X4ENTRYMAJ23Biological and physical science, science tech 0.0805061
X4ENTRYMAJ23Mathematics 0.0729173
X4ENTRYMAJ23Agriculture and natural resources 0.1474664
X4ENTRYMAJ23General studies and other 0.1499260
X4ENTRYMAJ23Social sciences 0.1688093
X4ENTRYMAJ23Psychology 0.1377309
X4ENTRYMAJ23Humanities 0.2607402
X4ENTRYMAJ23History 0.1475859
X4ENTRYMAJ23Personal and consumer services 0.1386387
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 0.4337423
X4ENTRYMAJ23Military technology and protective services 0.1482326
X4ENTRYMAJ23Health care fields 0.1591009
X4ENTRYMAJ23Business 0.1194903
X4ENTRYMAJ23Education 0.2294671
X4ENTRYMAJ23Architecture 0.2198331
X4ENTRYMAJ23Communications 0.2830411
X4ENTRYMAJ23Public administration and human services 0.1670796
X4ENTRYMAJ23Design and applied arts 0.2517047
X4ENTRYMAJ23Law and legal studies 0.2328264
X4ENTRYMAJ23Theology and religious vocations 0.3499678
X1FAMINCOMEFamily income > $15,000 and <= $35,000 0.0097161
X1FAMINCOMEFamily income > $35,000 and <= $55,000 0.0542806
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.1061207
X1FAMINCOMEFamily income > $75,000 and <= $95,000 0.0811145
X1FAMINCOMEFamily income > $95,000 and <= $115,000 0.1507057
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.1707281
X1FAMINCOMEFamily income > $135,000 and <= $155,000 0.1262002
X1FAMINCOMEFamily income > $155,000 and <=$175,000 0.0952562
X1FAMINCOMEFamily income > $175,000 and <= $195,000 0.1803418
X1FAMINCOMEFamily income > $195,000 and <= $215,000 0.2102978
X1FAMINCOMEFamily income > $215,000 and <= $235,000 0.1432016
X1FAMINCOMEFamily income > $235,000 0.1595624
X3TCREDAPIB 0.0292806
X1CONTROLCatholic or other private 0.0861247
Std. Error
(Intercept) 0.0618736
X1STU30OCC2Management Occupations 0.0575649
X1STU30OCC2Business and Financial Operations Occupations 0.0717997
X1STU30OCC2Computer and Mathematical Occupations 0.0645507
X1STU30OCC2Architecture and Engineering Occupations 0.0374192
X1STU30OCC2Life, Physical, and Social Science Occupations 0.0369491
X1STU30OCC2Community and Social Services Occupations 0.0866033
X1STU30OCC2Legal Occupations 0.0430488
X1STU30OCC2Education, Training, and Library Occupations 0.0419590
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations 0.0290267
X1STU30OCC2Healthcare Practitioners and Technical Occupations 0.0236654
X1STU30OCC2Healthcare Support Occupations 0.2132309
X1STU30OCC2Protective Service Occupations 0.0596469
X1STU30OCC2Food Preparation and Serving Related Occupations 0.0864662
X1STU30OCC2Personal Care and Service Occupations 0.0832071
X1STU30OCC2Sales and Related Occupations 0.1296512
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.2244406
X1STU30OCC2Construction and Extraction Occupations 0.1517391
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.1039421
X1STU30OCC2Production Occupations 0.1767864
X1STU30OCC2Transportation and Material Moving Occupations 0.1132055
X1STU30OCC2Military Specific Occupations 0.0686630
X3TGPAACAD 0.0136806
X4ENTRYMAJ23Computer and information sciences 0.0569549
X4ENTRYMAJ23Engineering and engineering technology 0.0469181
X4ENTRYMAJ23Biological and physical science, science tech 0.0450795
X4ENTRYMAJ23Mathematics 0.0965082
X4ENTRYMAJ23Agriculture and natural resources 0.0708381
X4ENTRYMAJ23General studies and other 0.0700379
X4ENTRYMAJ23Social sciences 0.0589234
X4ENTRYMAJ23Psychology 0.0548070
X4ENTRYMAJ23Humanities 0.0522431
X4ENTRYMAJ23History 0.0951975
X4ENTRYMAJ23Personal and consumer services 0.0608408
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 0.0726747
X4ENTRYMAJ23Military technology and protective services 0.0581589
X4ENTRYMAJ23Health care fields 0.0424604
X4ENTRYMAJ23Business 0.0434976
X4ENTRYMAJ23Education 0.0506218
X4ENTRYMAJ23Architecture 0.1211585
X4ENTRYMAJ23Communications 0.0602309
X4ENTRYMAJ23Public administration and human services 0.0927785
X4ENTRYMAJ23Design and applied arts 0.0832168
X4ENTRYMAJ23Law and legal studies 0.1223645
X4ENTRYMAJ23Theology and religious vocations 0.1661350
X1FAMINCOMEFamily income > $15,000 and <= $35,000 0.0424455
X1FAMINCOMEFamily income > $35,000 and <= $55,000 0.0416326
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.0416099
X1FAMINCOMEFamily income > $75,000 and <= $95,000 0.0425920
X1FAMINCOMEFamily income > $95,000 and <= $115,000 0.0438472
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.0467359
X1FAMINCOMEFamily income > $135,000 and <= $155,000 0.0492487
X1FAMINCOMEFamily income > $155,000 and <=$175,000 0.0596338
X1FAMINCOMEFamily income > $175,000 and <= $195,000 0.0714790
X1FAMINCOMEFamily income > $195,000 and <= $215,000 0.0635681
X1FAMINCOMEFamily income > $215,000 and <= $235,000 0.0904840
X1FAMINCOMEFamily income > $235,000 0.0503627
X3TCREDAPIB 0.0034555
X1CONTROLCatholic or other private 0.0199546
t value
(Intercept) 7.340
X1STU30OCC2Management Occupations 0.266
X1STU30OCC2Business and Financial Operations Occupations 1.090
X1STU30OCC2Computer and Mathematical Occupations -0.574
X1STU30OCC2Architecture and Engineering Occupations -1.564
X1STU30OCC2Life, Physical, and Social Science Occupations -0.825
X1STU30OCC2Community and Social Services Occupations 1.608
X1STU30OCC2Legal Occupations -1.714
X1STU30OCC2Education, Training, and Library Occupations 1.598
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations -0.175
X1STU30OCC2Healthcare Practitioners and Technical Occupations -1.280
X1STU30OCC2Healthcare Support Occupations 0.408
X1STU30OCC2Protective Service Occupations -0.880
X1STU30OCC2Food Preparation and Serving Related Occupations -2.725
X1STU30OCC2Personal Care and Service Occupations 1.181
X1STU30OCC2Sales and Related Occupations 0.335
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.522
X1STU30OCC2Construction and Extraction Occupations 0.465
X1STU30OCC2Installation, Maintenance, and Repair Occupations 1.221
X1STU30OCC2Production Occupations 0.845
X1STU30OCC2Transportation and Material Moving Occupations 1.123
X1STU30OCC2Military Specific Occupations -2.425
X3TGPAACAD 49.757
X4ENTRYMAJ23Computer and information sciences -0.072
X4ENTRYMAJ23Engineering and engineering technology 0.006
X4ENTRYMAJ23Biological and physical science, science tech 1.786
X4ENTRYMAJ23Mathematics 0.756
X4ENTRYMAJ23Agriculture and natural resources 2.082
X4ENTRYMAJ23General studies and other 2.141
X4ENTRYMAJ23Social sciences 2.865
X4ENTRYMAJ23Psychology 2.513
X4ENTRYMAJ23Humanities 4.991
X4ENTRYMAJ23History 1.550
X4ENTRYMAJ23Personal and consumer services 2.279
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 5.968
X4ENTRYMAJ23Military technology and protective services 2.549
X4ENTRYMAJ23Health care fields 3.747
X4ENTRYMAJ23Business 2.747
X4ENTRYMAJ23Education 4.533
X4ENTRYMAJ23Architecture 1.814
X4ENTRYMAJ23Communications 4.699
X4ENTRYMAJ23Public administration and human services 1.801
X4ENTRYMAJ23Design and applied arts 3.025
X4ENTRYMAJ23Law and legal studies 1.903
X4ENTRYMAJ23Theology and religious vocations 2.107
X1FAMINCOMEFamily income > $15,000 and <= $35,000 0.229
X1FAMINCOMEFamily income > $35,000 and <= $55,000 1.304
X1FAMINCOMEFamily income > $55,000 and <= $75,000 2.550
X1FAMINCOMEFamily income > $75,000 and <= $95,000 1.904
X1FAMINCOMEFamily income > $95,000 and <= $115,000 3.437
X1FAMINCOMEFamily income > $115,000 and <= $135,000 3.653
X1FAMINCOMEFamily income > $135,000 and <= $155,000 2.563
X1FAMINCOMEFamily income > $155,000 and <=$175,000 1.597
X1FAMINCOMEFamily income > $175,000 and <= $195,000 2.523
X1FAMINCOMEFamily income > $195,000 and <= $215,000 3.308
X1FAMINCOMEFamily income > $215,000 and <= $235,000 1.583
X1FAMINCOMEFamily income > $235,000 3.168
X3TCREDAPIB 8.474
X1CONTROLCatholic or other private 4.316
Pr(>|t|)
(Intercept) 2.37e-13
X1STU30OCC2Management Occupations 0.790004
X1STU30OCC2Business and Financial Operations Occupations 0.275615
X1STU30OCC2Computer and Mathematical Occupations 0.566241
X1STU30OCC2Architecture and Engineering Occupations 0.117775
X1STU30OCC2Life, Physical, and Social Science Occupations 0.409157
X1STU30OCC2Community and Social Services Occupations 0.107820
X1STU30OCC2Legal Occupations 0.086646
X1STU30OCC2Education, Training, and Library Occupations 0.110117
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations 0.861432
X1STU30OCC2Healthcare Practitioners and Technical Occupations 0.200493
X1STU30OCC2Healthcare Support Occupations 0.683603
X1STU30OCC2Protective Service Occupations 0.379042
X1STU30OCC2Food Preparation and Serving Related Occupations 0.006442
X1STU30OCC2Personal Care and Service Occupations 0.237801
X1STU30OCC2Sales and Related Occupations 0.737649
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.601633
X1STU30OCC2Construction and Extraction Occupations 0.641997
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.222111
X1STU30OCC2Production Occupations 0.398059
X1STU30OCC2Transportation and Material Moving Occupations 0.261353
X1STU30OCC2Military Specific Occupations 0.015321
X3TGPAACAD < 2e-16
X4ENTRYMAJ23Computer and information sciences 0.942325
X4ENTRYMAJ23Engineering and engineering technology 0.995420
X4ENTRYMAJ23Biological and physical science, science tech 0.074162
X4ENTRYMAJ23Mathematics 0.449940
X4ENTRYMAJ23Agriculture and natural resources 0.037401
X4ENTRYMAJ23General studies and other 0.032336
X4ENTRYMAJ23Social sciences 0.004183
X4ENTRYMAJ23Psychology 0.011992
X4ENTRYMAJ23Humanities 6.15e-07
X4ENTRYMAJ23History 0.121110
X4ENTRYMAJ23Personal and consumer services 0.022713
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 2.51e-09
X4ENTRYMAJ23Military technology and protective services 0.010831
X4ENTRYMAJ23Health care fields 0.000180
X4ENTRYMAJ23Business 0.006028
X4ENTRYMAJ23Education 5.91e-06
X4ENTRYMAJ23Architecture 0.069653
X4ENTRYMAJ23Communications 2.66e-06
X4ENTRYMAJ23Public administration and human services 0.071769
X4ENTRYMAJ23Design and applied arts 0.002498
X4ENTRYMAJ23Law and legal studies 0.057115
X4ENTRYMAJ23Theology and religious vocations 0.035193
X1FAMINCOMEFamily income > $15,000 and <= $35,000 0.818947
X1FAMINCOMEFamily income > $35,000 and <= $55,000 0.192342
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.010781
X1FAMINCOMEFamily income > $75,000 and <= $95,000 0.056891
X1FAMINCOMEFamily income > $95,000 and <= $115,000 0.000591
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.000261
X1FAMINCOMEFamily income > $135,000 and <= $155,000 0.010412
X1FAMINCOMEFamily income > $155,000 and <=$175,000 0.110231
X1FAMINCOMEFamily income > $175,000 and <= $195,000 0.011657
X1FAMINCOMEFamily income > $195,000 and <= $215,000 0.000943
X1FAMINCOMEFamily income > $215,000 and <= $235,000 0.113552
X1FAMINCOMEFamily income > $235,000 0.001540
X3TCREDAPIB < 2e-16
X1CONTROLCatholic or other private 1.61e-05
(Intercept) ***
X1STU30OCC2Management Occupations
X1STU30OCC2Business and Financial Operations Occupations
X1STU30OCC2Computer and Mathematical Occupations
X1STU30OCC2Architecture and Engineering Occupations
X1STU30OCC2Life, Physical, and Social Science Occupations
X1STU30OCC2Community and Social Services Occupations
X1STU30OCC2Legal Occupations .
X1STU30OCC2Education, Training, and Library Occupations
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations
X1STU30OCC2Healthcare Practitioners and Technical Occupations
X1STU30OCC2Healthcare Support Occupations
X1STU30OCC2Protective Service Occupations
X1STU30OCC2Food Preparation and Serving Related Occupations **
X1STU30OCC2Personal Care and Service Occupations
X1STU30OCC2Sales and Related Occupations
X1STU30OCC2Farming, Fishing, and Forestry Occupations
X1STU30OCC2Construction and Extraction Occupations
X1STU30OCC2Installation, Maintenance, and Repair Occupations
X1STU30OCC2Production Occupations
X1STU30OCC2Transportation and Material Moving Occupations
X1STU30OCC2Military Specific Occupations *
X3TGPAACAD ***
X4ENTRYMAJ23Computer and information sciences
X4ENTRYMAJ23Engineering and engineering technology
X4ENTRYMAJ23Biological and physical science, science tech .
X4ENTRYMAJ23Mathematics
X4ENTRYMAJ23Agriculture and natural resources *
X4ENTRYMAJ23General studies and other *
X4ENTRYMAJ23Social sciences **
X4ENTRYMAJ23Psychology *
X4ENTRYMAJ23Humanities ***
X4ENTRYMAJ23History
X4ENTRYMAJ23Personal and consumer services *
X4ENTRYMAJ23Manufacturing, construction, repair, transportation ***
X4ENTRYMAJ23Military technology and protective services *
X4ENTRYMAJ23Health care fields ***
X4ENTRYMAJ23Business **
X4ENTRYMAJ23Education ***
X4ENTRYMAJ23Architecture .
X4ENTRYMAJ23Communications ***
X4ENTRYMAJ23Public administration and human services .
X4ENTRYMAJ23Design and applied arts **
X4ENTRYMAJ23Law and legal studies .
X4ENTRYMAJ23Theology and religious vocations *
X1FAMINCOMEFamily income > $15,000 and <= $35,000
X1FAMINCOMEFamily income > $35,000 and <= $55,000
X1FAMINCOMEFamily income > $55,000 and <= $75,000 *
X1FAMINCOMEFamily income > $75,000 and <= $95,000 .
X1FAMINCOMEFamily income > $95,000 and <= $115,000 ***
X1FAMINCOMEFamily income > $115,000 and <= $135,000 ***
X1FAMINCOMEFamily income > $135,000 and <= $155,000 *
X1FAMINCOMEFamily income > $155,000 and <=$175,000
X1FAMINCOMEFamily income > $175,000 and <= $195,000 *
X1FAMINCOMEFamily income > $195,000 and <= $215,000 ***
X1FAMINCOMEFamily income > $215,000 and <= $235,000
X1FAMINCOMEFamily income > $235,000 **
X3TCREDAPIB ***
X1CONTROLCatholic or other private ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7035 on 7290 degrees of freedom
Multiple R-squared: 0.3613, Adjusted R-squared: 0.3562
F-statistic: 71.1 on 58 and 7290 DF, p-value: < 2.2e-16Diagnostics
Constant Variance
- Breusch-Pagan test yields a p-value < 0.0001.
studentized Breusch-Pagan test
data: MLR_all.reg.reduced
BP = 744.69, df = 58, p-value < 2.2e-16- Because the response variable is bound.
Diagnostics
Normality
Remedial Measures
Need to address non-constant variance first, and then recheck normality assumption
Try Box-Cox transformation
Weighted Least Squares
Recheck model diagnostics.
Box-Cox Residual Variance
Still a pattern
Weighted Least Squares
Better, but wider at higher GPAs.
Additional Remedial Measures
Implications & Limitations
Non-constant variance could not be addressed through transformation and other remedies given this set of predictors.
Perhaps other predictors not captured by the High School Longitudinal Study are more reliably related to College GPA and choice of future career.
Bound response variable.
Additionally, other regression approaches, such as Quantile regression, may be useful for exploring the significance of this relationship.
Appendix
- Results for WLS using fitted values
Call:
lm(formula = X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 +
X1FAMINCOME + X3TCREDAPIB + X1CONTROL, data = MLR_all_WLS_fitted,
weights = w1)
Weighted Residuals:
Min 1Q Median 3Q Max
-14.6182 -0.5521 0.1648 0.7707 6.6181
Coefficients:
Estimate
(Intercept) 0.535758
X1STU30OCC2Management Occupations 0.005601
X1STU30OCC2Business and Financial Operations Occupations 0.289747
X1STU30OCC2Computer and Mathematical Occupations -0.039280
X1STU30OCC2Architecture and Engineering Occupations -0.097886
X1STU30OCC2Life, Physical, and Social Science Occupations -0.116109
X1STU30OCC2Community and Social Services Occupations 0.012566
X1STU30OCC2Legal Occupations -0.214479
X1STU30OCC2Education, Training, and Library Occupations -0.156458
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations -0.059120
X1STU30OCC2Healthcare Practitioners and Technical Occupations -0.068958
X1STU30OCC2Healthcare Support Occupations -0.002941
X1STU30OCC2Protective Service Occupations -0.092789
X1STU30OCC2Food Preparation and Serving Related Occupations -0.180151
X1STU30OCC2Personal Care and Service Occupations -0.038598
X1STU30OCC2Sales and Related Occupations 0.098737
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.054912
X1STU30OCC2Construction and Extraction Occupations 0.016568
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.034441
X1STU30OCC2Production Occupations 0.065042
X1STU30OCC2Transportation and Material Moving Occupations -0.057941
X1STU30OCC2Military Specific Occupations -0.170100
X3TGPAACAD 0.702746
X4ENTRYMAJ23Computer and information sciences -0.040411
X4ENTRYMAJ23Engineering and engineering technology 0.002346
X4ENTRYMAJ23Biological and physical science, science tech -0.023939
X4ENTRYMAJ23Mathematics -0.063906
X4ENTRYMAJ23Agriculture and natural resources 0.116270
X4ENTRYMAJ23General studies and other 0.137157
X4ENTRYMAJ23Social sciences 0.093797
X4ENTRYMAJ23Psychology 0.244598
X4ENTRYMAJ23Humanities 0.012847
X4ENTRYMAJ23History 0.150005
X4ENTRYMAJ23Personal and consumer services -0.008015
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 0.212018
X4ENTRYMAJ23Military technology and protective services 0.074248
X4ENTRYMAJ23Health care fields 0.146836
X4ENTRYMAJ23Business 0.137890
X4ENTRYMAJ23Education 0.302495
X4ENTRYMAJ23Architecture -0.017487
X4ENTRYMAJ23Communications 0.206382
X4ENTRYMAJ23Public administration and human services 0.020229
X4ENTRYMAJ23Design and applied arts 0.242797
X4ENTRYMAJ23Law and legal studies 0.400407
X4ENTRYMAJ23Theology and religious vocations 0.462521
X1FAMINCOMEFamily income > $15,000 and <= $35,000 -0.018083
X1FAMINCOMEFamily income > $35,000 and <= $55,000 0.058854
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.027684
X1FAMINCOMEFamily income > $75,000 and <= $95,000 0.135304
X1FAMINCOMEFamily income > $95,000 and <= $115,000 0.137657
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.007124
X1FAMINCOMEFamily income > $135,000 and <= $155,000 0.240529
X1FAMINCOMEFamily income > $155,000 and <=$175,000 0.078095
X1FAMINCOMEFamily income > $175,000 and <= $195,000 0.130067
X1FAMINCOMEFamily income > $195,000 and <= $215,000 0.161867
X1FAMINCOMEFamily income > $215,000 and <= $235,000 0.071766
X1FAMINCOMEFamily income > $235,000 0.034238
X3TCREDAPIB 0.013686
X1CONTROLCatholic or other private 0.027121
Std. Error
(Intercept) 0.068433
X1STU30OCC2Management Occupations 0.038709
X1STU30OCC2Business and Financial Operations Occupations 0.043984
X1STU30OCC2Computer and Mathematical Occupations 0.054153
X1STU30OCC2Architecture and Engineering Occupations 0.032659
X1STU30OCC2Life, Physical, and Social Science Occupations 0.023208
X1STU30OCC2Community and Social Services Occupations 0.050039
X1STU30OCC2Legal Occupations 0.032430
X1STU30OCC2Education, Training, and Library Occupations 0.021656
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations 0.019580
X1STU30OCC2Healthcare Practitioners and Technical Occupations 0.016616
X1STU30OCC2Healthcare Support Occupations 0.196838
X1STU30OCC2Protective Service Occupations 0.063754
X1STU30OCC2Food Preparation and Serving Related Occupations 0.102229
X1STU30OCC2Personal Care and Service Occupations 0.074979
X1STU30OCC2Sales and Related Occupations 0.093405
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.183346
X1STU30OCC2Construction and Extraction Occupations 0.148358
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.103002
X1STU30OCC2Production Occupations 0.155835
X1STU30OCC2Transportation and Material Moving Occupations 0.096697
X1STU30OCC2Military Specific Occupations 0.081037
X3TGPAACAD 0.013766
X4ENTRYMAJ23Computer and information sciences 0.060206
X4ENTRYMAJ23Engineering and engineering technology 0.046388
X4ENTRYMAJ23Biological and physical science, science tech 0.043356
X4ENTRYMAJ23Mathematics 0.072199
X4ENTRYMAJ23Agriculture and natural resources 0.061818
X4ENTRYMAJ23General studies and other 0.075897
X4ENTRYMAJ23Social sciences 0.048019
X4ENTRYMAJ23Psychology 0.049888
X4ENTRYMAJ23Humanities 0.044288
X4ENTRYMAJ23History 0.083018
X4ENTRYMAJ23Personal and consumer services 0.063851
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 0.075856
X4ENTRYMAJ23Military technology and protective services 0.065336
X4ENTRYMAJ23Health care fields 0.043163
X4ENTRYMAJ23Business 0.043204
X4ENTRYMAJ23Education 0.045762
X4ENTRYMAJ23Architecture 0.083224
X4ENTRYMAJ23Communications 0.048907
X4ENTRYMAJ23Public administration and human services 0.068020
X4ENTRYMAJ23Design and applied arts 0.075142
X4ENTRYMAJ23Law and legal studies 0.099736
X4ENTRYMAJ23Theology and religious vocations 0.105580
X1FAMINCOMEFamily income > $15,000 and <= $35,000 0.047604
X1FAMINCOMEFamily income > $35,000 and <= $55,000 0.045443
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.043934
X1FAMINCOMEFamily income > $75,000 and <= $95,000 0.044682
X1FAMINCOMEFamily income > $95,000 and <= $115,000 0.044062
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.044652
X1FAMINCOMEFamily income > $135,000 and <= $155,000 0.044832
X1FAMINCOMEFamily income > $155,000 and <=$175,000 0.051208
X1FAMINCOMEFamily income > $175,000 and <= $195,000 0.059028
X1FAMINCOMEFamily income > $195,000 and <= $215,000 0.047617
X1FAMINCOMEFamily income > $215,000 and <= $235,000 0.068768
X1FAMINCOMEFamily income > $235,000 0.044393
X3TCREDAPIB 0.001930
X1CONTROLCatholic or other private 0.012888
t value
(Intercept) 7.829
X1STU30OCC2Management Occupations 0.145
X1STU30OCC2Business and Financial Operations Occupations 6.587
X1STU30OCC2Computer and Mathematical Occupations -0.725
X1STU30OCC2Architecture and Engineering Occupations -2.997
X1STU30OCC2Life, Physical, and Social Science Occupations -5.003
X1STU30OCC2Community and Social Services Occupations 0.251
X1STU30OCC2Legal Occupations -6.614
X1STU30OCC2Education, Training, and Library Occupations -7.225
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations -3.019
X1STU30OCC2Healthcare Practitioners and Technical Occupations -4.150
X1STU30OCC2Healthcare Support Occupations -0.015
X1STU30OCC2Protective Service Occupations -1.455
X1STU30OCC2Food Preparation and Serving Related Occupations -1.762
X1STU30OCC2Personal Care and Service Occupations -0.515
X1STU30OCC2Sales and Related Occupations 1.057
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.300
X1STU30OCC2Construction and Extraction Occupations 0.112
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.334
X1STU30OCC2Production Occupations 0.417
X1STU30OCC2Transportation and Material Moving Occupations -0.599
X1STU30OCC2Military Specific Occupations -2.099
X3TGPAACAD 51.050
X4ENTRYMAJ23Computer and information sciences -0.671
X4ENTRYMAJ23Engineering and engineering technology 0.051
X4ENTRYMAJ23Biological and physical science, science tech -0.552
X4ENTRYMAJ23Mathematics -0.885
X4ENTRYMAJ23Agriculture and natural resources 1.881
X4ENTRYMAJ23General studies and other 1.807
X4ENTRYMAJ23Social sciences 1.953
X4ENTRYMAJ23Psychology 4.903
X4ENTRYMAJ23Humanities 0.290
X4ENTRYMAJ23History 1.807
X4ENTRYMAJ23Personal and consumer services -0.126
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 2.795
X4ENTRYMAJ23Military technology and protective services 1.136
X4ENTRYMAJ23Health care fields 3.402
X4ENTRYMAJ23Business 3.192
X4ENTRYMAJ23Education 6.610
X4ENTRYMAJ23Architecture -0.210
X4ENTRYMAJ23Communications 4.220
X4ENTRYMAJ23Public administration and human services 0.297
X4ENTRYMAJ23Design and applied arts 3.231
X4ENTRYMAJ23Law and legal studies 4.015
X4ENTRYMAJ23Theology and religious vocations 4.381
X1FAMINCOMEFamily income > $15,000 and <= $35,000 -0.380
X1FAMINCOMEFamily income > $35,000 and <= $55,000 1.295
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.630
X1FAMINCOMEFamily income > $75,000 and <= $95,000 3.028
X1FAMINCOMEFamily income > $95,000 and <= $115,000 3.124
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.160
X1FAMINCOMEFamily income > $135,000 and <= $155,000 5.365
X1FAMINCOMEFamily income > $155,000 and <=$175,000 1.525
X1FAMINCOMEFamily income > $175,000 and <= $195,000 2.203
X1FAMINCOMEFamily income > $195,000 and <= $215,000 3.399
X1FAMINCOMEFamily income > $215,000 and <= $235,000 1.044
X1FAMINCOMEFamily income > $235,000 0.771
X3TCREDAPIB 7.091
X1CONTROLCatholic or other private 2.104
Pr(>|t|)
(Intercept) 5.62e-15
X1STU30OCC2Management Occupations 0.884959
X1STU30OCC2Business and Financial Operations Occupations 4.78e-11
X1STU30OCC2Computer and Mathematical Occupations 0.468253
X1STU30OCC2Architecture and Engineering Occupations 0.002734
X1STU30OCC2Life, Physical, and Social Science Occupations 5.78e-07
X1STU30OCC2Community and Social Services Occupations 0.801731
X1STU30OCC2Legal Occupations 4.02e-11
X1STU30OCC2Education, Training, and Library Occupations 5.53e-13
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations 0.002542
X1STU30OCC2Healthcare Practitioners and Technical Occupations 3.36e-05
X1STU30OCC2Healthcare Support Occupations 0.988080
X1STU30OCC2Protective Service Occupations 0.145596
X1STU30OCC2Food Preparation and Serving Related Occupations 0.078072
X1STU30OCC2Personal Care and Service Occupations 0.606724
X1STU30OCC2Sales and Related Occupations 0.290510
X1STU30OCC2Farming, Fishing, and Forestry Occupations 0.764566
X1STU30OCC2Construction and Extraction Occupations 0.911081
X1STU30OCC2Installation, Maintenance, and Repair Occupations 0.738110
X1STU30OCC2Production Occupations 0.676416
X1STU30OCC2Transportation and Material Moving Occupations 0.549057
X1STU30OCC2Military Specific Occupations 0.035848
X3TGPAACAD < 2e-16
X4ENTRYMAJ23Computer and information sciences 0.502109
X4ENTRYMAJ23Engineering and engineering technology 0.959663
X4ENTRYMAJ23Biological and physical science, science tech 0.580853
X4ENTRYMAJ23Mathematics 0.376115
X4ENTRYMAJ23Agriculture and natural resources 0.060033
X4ENTRYMAJ23General studies and other 0.070782
X4ENTRYMAJ23Social sciences 0.050818
X4ENTRYMAJ23Psychology 9.64e-07
X4ENTRYMAJ23Humanities 0.771755
X4ENTRYMAJ23History 0.070821
X4ENTRYMAJ23Personal and consumer services 0.900109
X4ENTRYMAJ23Manufacturing, construction, repair, transportation 0.005203
X4ENTRYMAJ23Military technology and protective services 0.255825
X4ENTRYMAJ23Health care fields 0.000673
X4ENTRYMAJ23Business 0.001421
X4ENTRYMAJ23Education 4.11e-11
X4ENTRYMAJ23Architecture 0.833582
X4ENTRYMAJ23Communications 2.47e-05
X4ENTRYMAJ23Public administration and human services 0.766174
X4ENTRYMAJ23Design and applied arts 0.001238
X4ENTRYMAJ23Law and legal studies 6.01e-05
X4ENTRYMAJ23Theology and religious vocations 1.20e-05
X1FAMINCOMEFamily income > $15,000 and <= $35,000 0.704064
X1FAMINCOMEFamily income > $35,000 and <= $55,000 0.195324
X1FAMINCOMEFamily income > $55,000 and <= $75,000 0.528634
X1FAMINCOMEFamily income > $75,000 and <= $95,000 0.002469
X1FAMINCOMEFamily income > $95,000 and <= $115,000 0.001790
X1FAMINCOMEFamily income > $115,000 and <= $135,000 0.873246
X1FAMINCOMEFamily income > $135,000 and <= $155,000 8.34e-08
X1FAMINCOMEFamily income > $155,000 and <=$175,000 0.127289
X1FAMINCOMEFamily income > $175,000 and <= $195,000 0.027592
X1FAMINCOMEFamily income > $195,000 and <= $215,000 0.000679
X1FAMINCOMEFamily income > $215,000 and <= $235,000 0.296712
X1FAMINCOMEFamily income > $235,000 0.440581
X3TCREDAPIB 1.46e-12
X1CONTROLCatholic or other private 0.035376
(Intercept) ***
X1STU30OCC2Management Occupations
X1STU30OCC2Business and Financial Operations Occupations ***
X1STU30OCC2Computer and Mathematical Occupations
X1STU30OCC2Architecture and Engineering Occupations **
X1STU30OCC2Life, Physical, and Social Science Occupations ***
X1STU30OCC2Community and Social Services Occupations
X1STU30OCC2Legal Occupations ***
X1STU30OCC2Education, Training, and Library Occupations ***
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations **
X1STU30OCC2Healthcare Practitioners and Technical Occupations ***
X1STU30OCC2Healthcare Support Occupations
X1STU30OCC2Protective Service Occupations
X1STU30OCC2Food Preparation and Serving Related Occupations .
X1STU30OCC2Personal Care and Service Occupations
X1STU30OCC2Sales and Related Occupations
X1STU30OCC2Farming, Fishing, and Forestry Occupations
X1STU30OCC2Construction and Extraction Occupations
X1STU30OCC2Installation, Maintenance, and Repair Occupations
X1STU30OCC2Production Occupations
X1STU30OCC2Transportation and Material Moving Occupations
X1STU30OCC2Military Specific Occupations *
X3TGPAACAD ***
X4ENTRYMAJ23Computer and information sciences
X4ENTRYMAJ23Engineering and engineering technology
X4ENTRYMAJ23Biological and physical science, science tech
X4ENTRYMAJ23Mathematics
X4ENTRYMAJ23Agriculture and natural resources .
X4ENTRYMAJ23General studies and other .
X4ENTRYMAJ23Social sciences .
X4ENTRYMAJ23Psychology ***
X4ENTRYMAJ23Humanities
X4ENTRYMAJ23History .
X4ENTRYMAJ23Personal and consumer services
X4ENTRYMAJ23Manufacturing, construction, repair, transportation **
X4ENTRYMAJ23Military technology and protective services
X4ENTRYMAJ23Health care fields ***
X4ENTRYMAJ23Business **
X4ENTRYMAJ23Education ***
X4ENTRYMAJ23Architecture
X4ENTRYMAJ23Communications ***
X4ENTRYMAJ23Public administration and human services
X4ENTRYMAJ23Design and applied arts **
X4ENTRYMAJ23Law and legal studies ***
X4ENTRYMAJ23Theology and religious vocations ***
X1FAMINCOMEFamily income > $15,000 and <= $35,000
X1FAMINCOMEFamily income > $35,000 and <= $55,000
X1FAMINCOMEFamily income > $55,000 and <= $75,000
X1FAMINCOMEFamily income > $75,000 and <= $95,000 **
X1FAMINCOMEFamily income > $95,000 and <= $115,000 **
X1FAMINCOMEFamily income > $115,000 and <= $135,000
X1FAMINCOMEFamily income > $135,000 and <= $155,000 ***
X1FAMINCOMEFamily income > $155,000 and <=$175,000
X1FAMINCOMEFamily income > $175,000 and <= $195,000 *
X1FAMINCOMEFamily income > $195,000 and <= $215,000 ***
X1FAMINCOMEFamily income > $215,000 and <= $235,000
X1FAMINCOMEFamily income > $235,000
X3TCREDAPIB ***
X1CONTROLCatholic or other private *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.113 on 7290 degrees of freedom
Multiple R-squared: 0.4581, Adjusted R-squared: 0.4537
F-statistic: 106.2 on 58 and 7290 DF, p-value: < 2.2e-16